SUSYQM, introduced by E. Witten in 1981, is the simplest example where supersymmetry can be dynamically broken [1]}. In spite of its initial character of a toy model; SUSYQM has earned importance in the recent decades, because it served as a starting point to the development of attractive theoretical features and concepts like shape invariance, isospectrality and factorization, that give new perspectives to old problems in quantum mechanics, like the integrability of the SE, see for example [2]}, [3]}, [4]} and the path integral formulation of classical mechanics [5]}. On the other hand, there is plenty of papers in
mathematical physics wherein DGT has been applied; see for example [6]}, [7]}, [8]}, [9]}, [10]}, [11]} for applications to study the non-integrability of Hamiltonian systems. For applications in the integrability of the SE, see [2]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}. For applications of differential Galois theory to other quantum integrable systems see [19]}, [20]}. The main Galoisian tools used in some of these papers are the Hamiltonian algebrization and the Kovacic's algorithm. These tools have led and still lead, to deduce exact solutions in several areas of mathematical physics.
